directx – Abnormal lighting when calculating in a tangent space. Probably something is wrong with the coordinate transformation matrix

I'm trying to calculate the lighting in a tangent space. But I continue to get abnormal results. I modified the demo code of the book and wondered if there was a problem with the transformation matrix I created.

I have trouble solving a problem in Introduction to 3D gaming programming with DirectX 11. I've tried using the TBN matrix

Tx, Ty, Tz,
Bx, By, Bz,
Nx, Ny, Nz

as shown in the book, but the light vector has been wrongly transformed into tangent space and I do not know how to debug this shader anymore.

Here is my Pixel Shader:

float4 PS1 (VertexOut pin,
uniform int gLightCount,
uniform bool gUseTexure,
uniform bool gAlphaClip,
uniform gFogEnabled bool,
uniform bool gReflectionEnabled): SV_Target {
// normal interpolation can make it non-normalized, so normalize it.
pin.NormalW = normalize (pin.NormalW);
pin.TangentW = normalize (pin.TangentW);

// The toEye vector is used in lighting.
float3 toEye = gEyePosW - pin.PosW;

// Hide the distance to the eye from this surface point.
float distToEye = length (toEye);

// Calculate normalMapSample
float3 normalMapSample =
normalize (SampledNormal2Normal (gNormalMap.Sample (samLinear, pin.Tex) .rgb));

// normalize toEye
toEye = normalize (toEye);

// Default value for multiplicative identity.
float4 texColor = float4 (1, 1, 1, 1);
if (gUseTexure)
{
// texture sample.
texColor = gDiffuseMap.Sample (samLinear, pin.Tex);

if (gAlphaClip)
{
// throw pixel if alpha texture < 0.1.  Note that we do this
        // test as soon as possible so that we can potentially exit the shader 
        // early, thereby skipping the rest of the shader code.
        clip(texColor.a - 0.1f);
    }
}

//
// Lighting.
//

float4 litColor = texColor;
if (gLightCount > 0)
{
// Begins with a sum of zero.
room float4 = float4 (0.0f, 0.0f, 0.0f, 0.0f);
float4 diffuse = float4 (0.0f, 0.0f, 0.0f, 0.0f);
float4 spec = float4 (0.0f, 0.0f, 0.0f, 0.0f);

// Sum the light contribution of each light source.  
    [unroll]
    for (int i = 0; i <gLightCount; ++ i)
{
float4 A, D, S;
ComputeDirectionalLightInTangent (gMaterial, gDirLights[i],
normalMapSample, World2TangentSpace (pin.NormalW, pin.TangentW, gTexTransform), toEye,
ADS);

ambient + = A;
diffuse + = D;
spec + = S;
}

litColor = texColor * (ambient + diffuse) + spec;

if (gReflectionEnabled)
{
float3 incident = -toEye;
float3 reflectionVector = reflect (incident, normalMapSample);
float4 reflectionColor = gCubeMap.Sample (samLinear, reflectVector);

litColor + = gMaterial.Reflect * reflectionColor;
}
}

//
// misting
//

if (gFogEnabled)
{
float fogLerp = saturate ((distToEye - gFogStart) / gFogRange);

// Mix the fog color and the lighted color.
litColor = lerp (litColor, gFogColor, fogLerp);
}

// Common to take the alpha of diffuse material and texture.
litColor.a = gMaterial.Diffuse.a * texColor.a;

returns litColor;
}  

And here is the function SampledNormal2Normal, World2TangentSpace and ComputeDirectionalLightInTangent:

float3 SampledNormal2Normal (float3 sampledNormal)
{
float3 normalT = 2.0f * sampledNormal - 1.0f;
normal returnT;
}

float3x3 World2TangentSpace (float3 unitNormalW, float3 tangentW, float4x4 texTransform)
{
// Build an orthonormal database.
float3 N = unitNormalW;
float3 T = normalize (tangent W - point (tangent W, N) * N);
float3 B = cross (N, T);

float3x3 TBN = float3x3 (T, B, N);
/ * float3x3 invTBN = float3x3 (T.x, T.y, T.z, B.x, B.y, B.z, N.x, N.y, N.z);
return invTBN; * /


float3 T_ = T - point (N, T) * N;
float3 B_ = B - point (N, B) * N - (point (T_, B) * T_) / point (T_, T_);
float3x3 invT_B_N = float3x3 (T_.x, T_.y, T_.z, B_.x, B_.y, B_.z, N.x, N.y, N.z);
return invT_B_N;
}

void ComputeDirectionalLightInTangent (Material Mat, DirectionalLight L,
float3 normalT, float3x3 toTS, float3 toEye,
on float4 ambient,
on diffuse float4,
off float4 spec)
{
// Initialize the outputs.
room = float4 (0.0f, 0.0f, 0.0f, 0.0f);
diffuse = float4 (0.0f, 0.0f, 0.0f, 0.0f);
spec = float4 (0.0f, 0.0f, 0.0f, 0.0f);

// The light vector aims in front of the direction of movement of the light rays.
float3 lightVec = -L.Direction;
lightVec = mul (lightVec, toTS);
lightVec = normalize (lightVec);

// toEye to Tangent Space
toEye = mul (toEye, toTS);
toEye = normalize (toEye);

// Add an ambient term.
ambient = mat.Ambient * L.Ambient;

// Add the diffuse and specular terms, provided the surface is in
// the line of light site.

float diffuseFactor = point (lightVec, normalT);

// Flatten to avoid dynamic connections.
[flatten]
if (diffuseFactor> 0.0f)
{
float3 v = reflect (-lightVec, normalT);
specFactor float = pow (max (dot (v, toEye), 0.0f), mat.Specular.w);

diffuse = diffuseFactor * mat.Diffuse * L.Diffuse;
spec = specFactor * mat.Specular * L.Specular;
}
}

The result I've got seems to be a lot darker in most places and too bright in many bright areas. I wonder if anyone can help me with my code or give me advice on how to debug an hlsl shald. My many thanks!

general topology – Continuity of a vector function $ f: X to mathbb {R ^ n} $, where $ X $ is a topological space.

Let $ X $ to be a topological space, and let $ f: X to mathbb {R ^ n} $ to be a vector function on $ X $. We define the $ k ^ {th} $ coordinating function of $ f $, which we refer to as $ f ^ k $, be $ p_k circ f $ or $ p_k: mathbb {R ^ n} to mathbb {R} $ is the $ k ^ {th} $ projection on $ mathbb {R ^ n} $. I've proved that if $ f $ is continuous, as is each coordinate function. However, I wonder if the opposite is true; which means that it is necessarily for $ f $ be continuous if each coordinate function is continuous ?.

I appreciate any help. Thank you in advance.

linux – How to fix a space allocation error on a machine with a lot of space?

I would like to run a template on RStudio Server, but I receive this error.

Error: Unable to allocate a 57.8 GB size vector

Here is what my data looks like and they have 10,000 lines.

            latitude longitude close_date close_price
1 1.501986 86.35068 2014-08-16 22: 25: 31.925431 1302246.3
2 36.367095 -98.66428 2014-08-05 06: 34: 00.165876 147504.5
36.599284 -97.92470 2014-08-12 23: 48: 00.887510 137400.6
4 67.994791 64.68859 2014-08-17 05: 27: 01.404296 -14112.0

This is my model.

library (caret)
training samples <- data$close_price %>%
createDataPartition (p = 0.8, list = FALSE)
train.data <- data[training.samples, ]
test.data <- datatraining.samples,]model <- train (
close_price ~., data = train.data, method = "knn",
trControl = trainControl ("cv", number = 1),
preProcess = c ("center", "scale"),
tuneLength = 1
)

My EC2 instance has more than 57 GB available. This is the memory.

                                                    total used cached free shared buffers
Mem: 65951628 830424 65121204 64 23908 215484
- / + buffers / cache: 591032 65360596
Exchange: 0 0 0

And it also has sufficient storage space. This is the hard disk space.

File System 1K-blocks Used Available Use% Installed on
devtmpfs 32965196 64 32965132 1% / dev
tmpfs 32975812 0 32975812 0% / dev / shm
/ dev / xvda1 103079180 6135168 96843764 6% /

And these are details about the machine.

R version 3.5.3 (2019-03-11)
Platform: x86_64-pc-linux-gnu (64 bit)
Run under: Amazon Linux AMI 2018.03

dg.differential geometry – Outer Derivative on Loop Space

notations:

Let $ X $ to be a multiple, and denote by $ LX: = C ^ infty (S ^ 1, X) $ its loop space. For a loop $ gamma in LX $ we can think of the tangent space of $ LX $ At this point $ gamma $ as space loops that are 'arbitrarily closed' at $ gamma $. This motivates the following definition

$$ T _ { gamma} LX: = Gamma (S ^ 1, gamma ^ * TX), $$

or $ Gamma (S ^ 1, gamma ^ * TX) $ indicate the space of the withdrawal package section
$ require {AMScd} $
begin {CD}
gamma ^ * TX @ >>> TX \
@V V V @VV V \
S ^ 1 @ >> gamma> X.
end {CD}

This is the description of the tangent package $ TLX to LX $ of the loop space of $ X $. By definition a $ kdifferential form on $ LX $ is a section of $ k ^ {th} $ external power of $ TLX $,
$$ Omega ^ k (LX): = Gamma (LX, Lambda ^ kTLX). $$

Question:

How is the external differential $ d $ defined for differential forms on the loop space?
begin {CD}
Omega ^ k (LX) @> d >> Omega ^ {k + 1} (LX)
end {CD}

partitioning – how to add unallocated space in the root partition of ubuntu

I know this question has been answered several times
but i have a different case enter the description of the image here

as in my case, I have an unallocated space of 97.66Gib and I want to add it to ext4 which is my root partition the unallocated space is above ext4 I can not resize it
as according to these tutorials

https://www.youtube.com/watch?v=QSpGaeHlkoE

please guide me how can i do it

general topology – Link between the topological dimension and the Hammel dimension (algebraic) of a vector space

I was wondering if there was a connection between these two dimension definitions in the case of a topological vector space. In fact, I know that the topological dimension sometimes coincides with other notions of dimension.

In addition, are there any interesting results on TVS coverage properties (such as paracompact, refinements, etc.)?

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webgl – view space of gl_FragCoord

Try to get the sample code so that CalcEyeFromWindow () (the first on the page) works in WebGL, but without success.

Associates the code with the following with explicit values ​​in case something goes wrong with the parameter pass. Visualize the output on a radius sphere, centered in the view and 3 units of the camera. Use step () in the output to provide sharp color transitions on the sphere.

The current exit is black. If I set the step to 0 for X and Y, the transitions for X and Y are centered on the sphere, so it seems that the problem is due at least in part to the calculation of clipPos.w.

Vertex shader:

high-precision float;

attribute vec3 a_position;

uniform mat4 u_modelMatrix;
uniform mat4 u_viewMatrix;
uniform mat4 u_projectionMatrix;


void main ()
{
gl_Position = u_projectionMatrix * u_viewMatrix * u_modelMatrix * vec4 (a_position, 1.0);
}

Fragment of shader:

high-precision float;

uniform mat4 u_inverseProjectionMatrix;
uniform mat4 u_projectionMatrix;

vec3 CalcEyeFromWindow (void)
{
vec3 ndcPos;
// Position of the fixed code window space on gl_FragCoord
// Dimensions of the code window
ndcPos.xy = (2.0 * gl_FragCoord.xy) / vec2 (1000, 500) - 1.
// Cut depths of the hard code
ndcPos.z = (2.0 * gl_FragCoord.z ​​- 1. - 4.) / (4. - 1.);

vec4 clipPos;
clipPos.w = u_projectionMatrix[3][2]    /
(ndcPos.z - (u_projectionMatrix[2][2]    / u_projectionMatrix[2][3]));
clipPos.xyz = ndcPos * clipPos.w;

return (u_inverseProjectionMatrix * clipPos) .xyz;
}

void main () {
// Step to clarify the position
gl_FragColor = vec4 (step (vec3 (.5, .5, 2.2), CalcEyeFromWindow () *)
vec3 (1,1, -1)), 1.);
}